Question

the following augmented matrix is in row-echelon form and represents a linear system. solve the system by using back-substitution if possible.

Answer 1

Given the matrix:

Given that it represents a linear system, we have the set of equations:

(1)x + 3y = 6

0x + (1)y = -1

x + 3y = 6..................equation 1

y = -1.........................equation 2.

Let's solve the system using substitution method.

Substitute -1 for y in equation 1:

x + 3(-1) = 6

x + (-3) = 6

x - 3 = 6

Add 3 to both sides:

x - 3 + 3 = 6 + 3

x = 9

From equation 2, we have the value of y:

y = -1

Therefore, the solution to the system is:

x = 9, y = -1

In point form:

(x, y) ==> (9, -1)

ANSWER:

x = 9, y = -1